It's model 4020pk without the hardware. If you'd rather cut the height than twist to adjust it, part 87 or 89, depending on which flapper you like. You can try your local hardware store, or call Korky (1-800-LAVELLE) and ask 'em where you can get the part you want near you.
Doesn't sound like there's any particular reason to replace the flush valve, assuming that a standard flapper fits on it, but it's chicken soup (i.e. can't hurt) as long as you have the thing apart. One concern about the Fluidmaster flush valve is that it may have a non-standard flapper, so I personally would scratch that idea, because I would want to use a Korky flapper, and the Korky flush valve will take a generic flapper, including the Korky and Korky Plus.